SOLUTION: if the height of an equilateral triangle is also a root of the equation y^4-3y^2-270, then the area of the triangle is, in cm3

Algebra ->  Trigonometry-basics -> SOLUTION: if the height of an equilateral triangle is also a root of the equation y^4-3y^2-270, then the area of the triangle is, in cm3      Log On


   

Question 1106512: if the height of an equilateral triangle is also a root of the equation y^4-3y^2-270, then the area of the triangle is, in cm3
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
That's not an equation.
I can tell, there's no equal sign.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


y%5E4-3y%5E2-270+=+%28y%5E2-18%29%28y%5E2%2B15%29+=+0

y%5E2=18 or y%5E2+=+-15.

Obviously we need to choose the positive real root.

So the height of the equilateral triangle is 3%2Asqrt%282%29.

The altitude of the equilateral triangle divides the triangle into two 30-60-90 right triangles. So the length of one-half the base is %283%2Asqrt%282%29%29%2Fsqrt%283%29.

Then the area of the triangle is one-half base times height: